The present invention relates to a method of controlling the transfer of a variety of information such as instruction information or data information between a memory or a peripheral circuit and a data processor, and a peripheral circuit, a data processor and a data processing system using the method, and, more particularly, to a technique which is especially effective if applied to the control technique of the data transfer between the data processor and a memory. Incidentally, the data processor in the present Specification will cover the general concept of a CPU (i.e., Central Processing Unit), a microprocessor, a microcomputer, a single-chip microcomputer, a digital-signal processor or a direct memory access controller.